Dislocations force

Forces acting on dislocations Force by external shear stress... 

We have considered briefly the important macroscopic description of a solid adsorbent, namely, its speciflc surface area, its possible fractal nature, and if porous, its pore size distribution. In addition, it is important to know as much as possible about the microscopic structure of the surface, and contemporary surface spectroscopic and diffraction techniques, discussed in Chapter VIII, provide a good deal of such information (see also Refs. 55 and 56 for short general reviews, and the monograph by Somoijai [57]). Scanning tunneling microscopy (STM) and atomic force microscopy (AFT) are now widely used to obtain the structure of surfaces and of adsorbed layers on a molecular scale (see Chapter VIII, Section XVIII-2B, and Ref. 58). On a less informative and more statistical basis are site energy distributions (Section XVII-14) there is also the somewhat laige-scale type of structure due to surface imperfections and dislocations (Section VII-4D and Fig. XVIII-14). 

Bone Fractures. A dislocation occurs when sudden pressure or force pulls a bone out of its socket at the joint. This is also known as subluxation. Bone fractures are classified into two categories simple fractures and compound, complex, or open fractures. In the latter the skin is pierced and the flesh and bone are exposed to infection. A bone fracture begins to heal nearly as soon as it occurs. Therefore, it is important for a bone fracture to be set accurately as soon as possible. 

We prove this by a virtual work calculation. We equate the work done by the applied stress when the dislocation moves completely through the crystal to the work done against the force / opposing its motion (Fig. 9.12). The upper part is displaced relative to the lower by the distance b, and the applied stress does work (7/1/2) moving... 

A crystal yields when the force xh (per unit length) exceeds /, the resistance (a force per unit length) opposing the motion of a dislocation. This defines the dislocation yield strength... 

How does this unlocking occur Figure 19.1 shows a dislocation which cannot glide because a precipitate blocks its path. The glide force rb per unit length, is balanced by the reaction /o from the precipitate. But unless the dislocation hits the precipitate at its mid-plane (an unlikely event) there is a component of force left over. It is the component ib tan 0, which tries to push the dislocation out of its slip plane. 

The dislocation cannot glide upwards by the shearing of atom planes - the atomic geometry is wrong - but the dislocation can move upwards if atoms at the bottom of the half-plane are able to diffuse away (Fig. 19.2). We have come across Fick s Law in which diffusion is driven by differences in concentration. A mechanical force can do exactly the same thing, and this is what leads to the diffusion of atoms away from the... 

The dependence of creep rate on applied stress a is due to the climb force the higher CT, the higher the climb force jb tan 0, the more dislocations become unlocked per second, the more dislocations glide per second, and the higher is the strain rate. 

As the stress is reduced, the rate of power-law creep (eqn. (19.1)) falls quickly (remember n is between 3 and 8). But creep does not stop instead, an alternative mechanism takes over. As Fig. 19.4 shows, a polycrystal can extend in response to the applied stress, ct, by grain elongation here, cr acts again as a mechanical driving force but, this time atoms diffuse from one set of the grain faces to the other, and dislocations are not involved. At high T/Tm, this diffusion takes place through the crystal itself, that... 

Similarly, in studies of lamellar interfaces the calculations using the central-force potentials predict correctly the order of energies for different interfaces but their ratios cannot be determined since the energy of the ordered twin is unphysically low, similarly as that of the SISF. Notwithstcinding, the situation is more complex in the case of interfaces. It has been demonstrated that the atomic structure of an ordered twin with APB type displacement is not predicted correctly in the framework of central-forces and that it is the formation of strong Ti-Ti covalent bonds across the interface which dominates the structure. This character of bonding in TiAl is likely to be even more important in more complex interfaces and it cannot be excluded that it affects directly dislocation cores. 

The central role of imperfections in mechanistic interpretations of decompositions of solids needs emphasizing. Apart from melting (which requires redistribution of all crystal-bonding forces, by a mechanism which has not yet been fully established) the decompositions of most solids involve the participation of atypical lattice constituents, structural distortions and/or surfaces. Such participants have, in particular instances, been identified with some certainty (e.g. excitons are important in the decompositions of some azides, dislocations are sites of nucleation in dissociations of a number of hydrates and carbonates). However, the... 

The mobilities of dislocations are determined by interactions between the atoms (molecules) within the cores of the dislocations. In pure simple metals, the interactions between groups of adjacent atoms depend very weakly on the configuration of the group, since the cohesive forces depend almost entirely on the local electron density, and are of long range. 

In covalently bonded crystals, the forces needed to shear atoms are localized and are large compared with metals. Therefore, dislocation motion is intrinsically constrained in them. 

Early in the history of crystal dislocations, the lack of resistance to motion in pure metal-like crystals was provided by the Bragg bubble model, although it was not taken seriously. By adjusting the size of the bubbles in a raft, it was found that the elastic behavior of the raft could be made comparable with that of a selected metal such as copper (Bragg and Lomer, 1949). In such a raft, it was further found that, as expected, the force needed to form a dislocation is large. However, the force needed to move a bubble is too small to measure. 

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